Question: What is the effect of gamma radiation (characterised by dose amount and dose rate) on the number of chromosomal abnormalities?

About the data
  • The data is from Purott and Reeder (1976) where an experiment was conducted to determine the effect of gamma radiation on chromosomal abnormalities.
  • The data recorded:
    • ca: the number of chromosomal abnormalities
    • cells: the number of cells
    • doseamt: the dose amount
    • doserate: the dose rate

Load the data

  • Is this data experimental or observational?

Explore the data

  • What are the combination of doseamt and doserate that was used?
Answer There are 9 levels of doserate spanning from 0.1 to 4 and 3 levels of doseamt (1, 2.5, 5).
  • doseamt and doserate are recorded as numeric variables. Should we consider it as categorical variables?
Answer

The effect of the doserate may be multiplicative (as indicated by the increasing spread) so we can consider taking the log of the variable and consider its interaction with doseamt.

There are only 3 levels of the doseamt and the quantity doesn’t appear to be linearly related to the response rate. We can consider taking it as a categorical variable.

Model the data

  • Let’s consider using a linear model for the rate of chromosomal abnormalities. What proportion of the variation does the model explain?
Answer

Remember that you can find the proportion of (response) variation that the model explains from the coefficient of determination (or \(R^2\)). The value is 0.9874, which is quite high and suggest that model fits well.

  • Let’s check residual plot for model diagnostics. Do you see any issues from the residual plot?
Answer

The variance does not appear to be constant as we see that the spread of the residuals is larger as the fitted value increases.

  • Let’s fit a Poisson regression instead. What is the default link for Poisson regression?

  • Now try fitting the Poisson regression model to this data.

Answer